The initiation and maintenance of a continental ice sheet are investigated using the GENESIS global climate model. A necessary condition for ice sheet initiation is to have snow cover survive through the summer. Model simulations examine the sensitivity of the maintenance of summer snow cover to the prescriptions of topography and solar luminosity. The time period chosen for this study is the Late Carboniferous (306 Ma) when an extensive continental ice sheet, as large if not larger than the Pleistocene glaciations, existed on a supercontinent in the southern hemisphere. This ice sheet, persisting for over 60 m.y., was one of the most prolonged periods of continuous glaciation in Earth history. Model simulations indicate that given the geography, solar luminosity (3% less than present), and atmospheric CO2 (same as present) estimated for this time period, summer snow cover remains as far equatorward as 35 ¿S latitude. Global mean temperature is -2.4 ¿C, 17.2 ¿C cooler than for present. Probable regions for the initiation of the Carboniferous ice sheet are apparent in analysis of the spin-up of the model to equilibrium. Summer snow cover first persists along the polar coastline of the supercontinent during year 4 of the simulation. Summer snow cover shows the greatest sensitivity to solar luminosity. Increasing the solar constant to its present value from the Late Carboniferous value results in a summer warming of southern hemisphere high-latitude land areas by as much as 37 ¿C and complete melting of any summer snow cover. Topography plays a lesser role. Reducing land elevations to sea level causes persistent summer snow cover to retreat only 8¿ poleward. Conversely, initializing the model with an elevated land ice sheet has no effect on summer snow cover extent. ¿ American Geophysical Union 1996